Research Experiences in Parallel Numerical Linear Algebra

该项目的目标是挑选那些很少或没有研究机会的本科生，为他们提供重要的研究经验，以激发他们对数学和计算科学的兴趣，使他们对参加研究生院继续教育和研究数学相关领域的可能性做出积极的反应。选择该项目是为了说明研究方法，这些方法将带领学生逐步从问题的定义，通过目标陈述，文献检索和实际研究，到撰写结果和结论。在这个项目中，学生将有机会对科学和工程中不同领域出现的问题进行数值算法领域的研究。特别是，学生将参与设计，分析和实现并行数值算法，以解决大型稀疏线性系统，特征值，最小二乘，优化问题。这项研究将包括调查这些领域的当前文献，以及可用于该项目的并行架构。在项目的教学阶段，学生还将学习数值线性代数、消息传递接口（MPI）和C/ c++编程语言中的数学概念，并通过适当的语言扩展提供在并行处理器上实现并行数值算法的方法。

The goal of this project is to take selected undergraduate students, who have had limited or no opportunities for research, and provide them with a significant research experience that will stimulate their interest in mathematical and computational sciences to the point that they will react positively to the possibility of attending graduate school for further education and research in mathematics realted areas. The project is selected to illustrate methods of research that will take the students progressively from the definition of the problem, though the statement of objectives, literature search, and the actual research, to the point of writing up their results and conclusions.In this project, students will be given an opportunity to do research in the area of numerical algorithms for problems arising from different areas in science and engineering. In particular, students will be involved in the design, analysis, and implementation of parallel numerical algorithms for the solution of large sparse linear systems, eigenvalue, least squares, optimization problems. This research will involve investigating the current literature in these areas as well as the parallel architecturs that can be utilized for this project. In the instructional phase of the project, students will also learn mathematical concepts in numerical linear algebra, message-passing interface (MPI) and C/C++ programming language with appropriate language extensions to provide a means of implementing the parallel numerical algorithms on parallel processors.